面向含未知输入受控动力系统的自适应稳定性约束神经微分方程
Adaptive Stability-Constrained Neural Differential Equations for Controlled Dynamical Systems with Unknown Inputs
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中文总结 AI 辅助
针对含未知输入的受控动力系统，本文提出自适应稳定性约束神经微分方程AS-NDE，推导了相关稳定性界，并给出针对达芬振荡器和PMSM模型的可复现评估方案，为后续实验提供技术起点。
中文摘要 AI 辅助
连续时间神经模型在非线性系统辨识中颇具吸引力，但当学习得到的向量场在与训练时不同的输入下展开时，微小的一步误差会迅速放大。本文针对带有测量控制量和不匹配未知扰动的系统，提出一种自适应稳定性约束神经微分方程（AS-NDE）。联合学习名义向量场和依赖于状态-输入的黎曼度量，通过构造保证其正定性，同时采用采样微分不等式对违反规定收缩率的情况进行惩罚。推导得到增量输入-状态界：两条轨迹间的距离呈指数衰减，衰减程度由它们的控制量和扰动的差异所决定。该表述明确考虑了依赖于输入的度量的时间导数项，这一项在启发式稳定性正则化器中极易被忽略。本文针对受迫达芬振荡器和永磁同步电机（PMSM）模型给出了可复现的评估方案。由于本稿件未附带实测数据或已执行的训练运行，所有数值曲线和表格均明确标注为说明性合成占位符；其PGFPlots坐标已嵌入源文件，可直接替换。本手稿旨在作为技术一致的起点，而非在规定实验开展前证明其经验优越性。
英文摘要
Continuous-time neural models are attractive for identifying nonlinear systems, but a small one-step error can grow rapidly when a learned vector field is rolled out under inputs that differ from those used for training. This paper develops an adaptive stability-constrained neural differential equation (AS-NDE) for systems with measured controls and unmatched, unknown perturbations. The nominal vector field and a state--input-dependent Riemannian metric are learned jointly. Positive definiteness is enforced by construction, while a sampled differential inequality penalizes violations of a prescribed contraction rate. An incremental input-to-state bound is derived: the distance between two trajectories decays exponentially up to gains determined by differences in their controls and disturbances. The statement explicitly accounts for the time derivative of an input-dependent metric, a term that is easily omitted in heuristic stability regularizers. We give a reproducible evaluation protocol for a forced Duffing oscillator and a permanent-magnet synchronous motor (PMSM) model. Because no measured data or executed training runs accompany this draft, all numerical curves and tables are clearly identified as illustrative synthetic placeholders; their PGFPlots coordinates are embedded in the source for direct replacement. The resulting manuscript is intended as a technically consistent starting point, not as evidence of empirical superiority before the prescribed experiments are run.
